Functions of Many Variables
Functions with more than one independent variable.
y=f(x) => one independent variable.
Not just price, but incomes, ect. are independent.
z=f(x, y) Here, z = dependent, x & y = independent.
z=e2x+3y Expediential fn.
Example 1: z=150-2x-3y
X-Intercept (z=0, y=0)
=> x=150/2 =75 (75, 0, 0)
Y-Intercept (x=0, z=0)
y= 150/3 = 50
Z-Intercept (x=0, y=0)
How dependent variable will a change as a result of the change in independent variables.
Use partial derivatives z=f(x, y)
Terms: Change: Δ, Delta: δ
To what effect a change in x has on z while holding y constant.
To what effect a change in y has on z while holding x constant.
=3x2+6xy2 Constant Multiplication Remains.
fy= 0+(3x2)(2)y+3y2 ->2 = (3-2)
fx Slope of fn with respect to x.
fy Slope of fn with respect to y.
When x=25, y=9
Plug in values= (0.5)(25)0.5(9)-0.5 = 5/6
Example 3: z=3x2y3
fx= (3y3)(2)x = 6xy3
fy= (3x2)3y2 = 9x2y2
Example 4: z=5x3-3x2y2+7y5
Example 5: z=(3x+5)(2x+6y)
Take derivative of 1st term with respect to x. Do not differentiate 2nd term of multiplication.
Example 6: Q=36KL-2K2-3L2 Production Function
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Copyright © 2016 Zoë-Marie Beesley
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